Asymptotically additive families of functions and a physical equivalence problem for flows

The paper proves the existence of a single continuous b with (1/t)||a_t−∫_0^t b∘φ_s ds||_∞→0 for suspension (hence hyperbolic) flows via a reduction to discrete time and Cuneo’s theorem. The candidate solution gives a short, general argument that works for any continuous flow on a compact space: introduce the seminorm δ(f)=limsup_t (1/t)||S_t f||_∞, prove δ(f)=sup_{μ∈M_Φ}|∫ f dμ|, complete the quotient C(Y)/{δ=0}, and take limits of approximants b_ε. This yields a single b without any suspension or expansiveness assumptions, contradicting the paper’s positioning of the “general flows” case as open. Hence the paper’s scope is incomplete relative to the model’s solution, while the model’s proof is correct.